Rarities (copied from http://weissschwarz.wikia.com/wiki/Card_Number):
C (Common): Four in each Booster Pack.
CC (Climax Common): There are 8 pairs per box.
CR (Climax Rare): One of each per booster box. So each booster box has one copy of all the CR cards.
R (Rare): Fifteen in each booster box.
RR (Double Rare): Four (One of each card color) are included per booster box.
RRR (Triple Rare): Holo-foil cards, most of these feature new descriptions and art. Only 4 of these are included in a booster carton.
SP (Special): Holo-foil CC/CR cards or cards with signatures. Only 2 of these are included in a booster carton.
SR (Special Rare): Holo-foil cards, without different descriptions or art. Ten of these are included in a booster carton
TD (Trial Deck): All Trial Deck cards are this rarity, many of them with parallel U or C rarity versions. There are also a number of Trial Deck only cards.
U (Uncommon): Two in each Booster Pack.

Nicknames:
Suicide/Suicider: A character that can reverse its Battle Opponent when it is Reversed. Example: "When this becomes Reversed, if its Battle Opponent is Level 0 or lower, you may Reverse that Character." Some characters have variations of this, such as putting the opponent in Stock instead of Reversing it.
Mill/Milling: Discarding cards from a Library to the Waiting Room. Example: Brainstorm keyword
Healing: Moving a card from Clock into (usually) the Waiting Room.
Vanilla: A card with no effect. Example: 0/0 3000 characters.
Stick: When damage isn't canceled by a climax, it "sticks".
1k1: A climax that gives +1000 power and 1 soul to all your characters. Often has interesting Trigger icons.
2k1: A climax that draws a card and gives +2000 power and 1 soul to one character. Always has 2 Soul Triggers.

Know of any other common abbreviations or nicknames? Let me know and I'll get them added to the list ASAP.